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The doehlert-klee problem: Part I, statistical background

  • R. G. Stanton
Invited Addresses
Part of the Lecture Notes in Mathematics book series (LNM, volume 686)

Keywords

Orthogonal Basis Balance Incomplete Block Design Distance Pattern Voronoi Polyhedron Pairwise Balance Design 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Conner, W.S., Jr., "On the Structure of Balanced Incomplete Block Designs", Ann. Math. Stat. 23 (1952), 52–71.MathSciNetGoogle Scholar
  2. [2]
    Collens, R.J., "Constructing BIBD's with a Computer", Ars Combinatoria 2 (1976), 285–303.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Doehlert, D.H., "Uniform Shell Designs", J. Royal Stat. Soc. C, 19 (1970), 231–239.Google Scholar
  4. [4]
    Doehlert, D.H. and Klee, V.L., "Experimental Designs Through Level Reduction of the d-dimensional Cuboctahedron", Discrete Math. 2 (1972), 309–334.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    McCarthy, D. and Vanstone, S.A., "On the Structure of Regular Pairwise Balanced Designs", submitted to Discrete Math.Google Scholar
  6. [6]
    McCarthy, D., Stanton, R.G. and Vanstone, S.A., "On an Extremal Class of (r, λ) Designs Related to a Problem of Doehlert and Klee", Ars Combinatoria 2 (1976).Google Scholar
  7. [7]
    Plackett, R.L. and Burman, J.P., "The Design of Optimum Multifactor Experiments", Biometrika 33 (1946), 305–325.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Stanton, R.G., "Results on (r, λ) Designs", Cong. Num. 18 (Proc. 6th Manitoba Conf. on Numerical Maths.), Winnipeg (1976), 411–412.Google Scholar
  9. [9]
    Stanton, R.G., "Some Results on Block Lengths in (r, λ) Designs", Ars Combinatoria 2 (1976), 213–219.MathSciNetzbMATHGoogle Scholar
  10. [10]
    Stanton, R.G. and Vanstone, S.A., "Further Results on a Problem of Doehlert and Klee", to appear, Utilitas Math.Google Scholar
  11. [11]
    Stanton, R.G. and Vanstone, S.A., "On a Problem of Doehlert and Klee", Cong. Num. 19 (Proc. Eighth S.E. Conf. on Combinatorics, Graph Theory, and Computing)", Baton Rouge (1977) to appear.Google Scholar
  12. [12]
    Stanton, R.G. and Vanstone, S.A., "Some Lower Bounds on the Size of Doehlert-Klee Designs", to appear, Ars Combinatoria.Google Scholar
  13. [13]
    Stanton, R.G. and Vanstone, S.A., "Some Theorems on DK Designs", preprint.Google Scholar
  14. [14]
    Scheffé, H., "The Simplex-centroid Design for Experiments with Mixtures", J. Royal Stat. Soc. B, 25(1963), 235–263.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • R. G. Stanton
    • 1
  1. 1.Computer Science DepartmentUniversity of ManitobaWinnipegCanada

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